Array-compressed parallel transmit pulse design with optimized coil-channel assignments and coil pruning for simultaneous multislice and 3D reduced-field-of-view excitations
Zhipeng Cao1,2, Xinqiang Yan1,3, and William A. Grissom1,2,3

1Vanderbilt University Insitute of Imaging Science, Vanderbilt University, Nashville, TN, United States, 2Biomedical Engineering, Vanderbilt University, Nashville, TN, United States, 3Radiology, Vanderbilt University, Nashville, TN, United States

Synopsis

An improved array-compressed parallel transmit pulse design is proposed and validated to optimally connect transmit arrays with a large number of elements to a few transmit channels. It is further demonstrated to achieve better performance with array-compressed coil designs than conventional designs for multiband RF shimming for human brain imaging and 3D spatially selective excitation for human occipital lobe imaging.

INTRODUCTION

Recently, array-compressed parallel transmission (acpTx) has been proposed as a low-cost solution to optimally drive a large number of transmit coils using a small number of transmit channels [1,2]. Figure 1 shows the proposed embodiment of acpTx [2], in which each transmit channel’s pulse is split across multiple transmit coils, and each coil receives the attenuated and phase shifted pulse. Compared to more general ones, this configuration has significant hardware simplicity with little penalty in pulse performance [1] . However, how to optimally assign coils to channels remains a question. Here we present an algorithm to jointly optimize coil-channel assignments along with acpTx pulse design, and to prune unnecessary coils. The method is validated and applied to simultaneous multislice and 3D-reduced FOV excitations, where the compressed many-coil arrays can outperform conventional arrays with the same number of input channels.

THEORY

The proposed acpTx pulse design with optimized coil-channel assignments is formulated as: $$\textrm{minimize } \phi(B); \textrm{s.t. rank}(B(\Theta_i)) = 1 (i = 1,...,N_{chan}) \textrm{ (Eqn 1)}$$ where $$$\phi$$$ is the pulse design cost function, $$$B$$$ the $$$N_t$$$ by $$$N_{coils}$$$ RF pulse matrix where $$$N_t$$$ is the number of pulse time points, $$$\Theta_i$$$ the coil-channel assignment vectors (1 vector for each input channel) that map the $$$N_{coils}$$$ transmit coils to the $$$N_{chan}$$$ input transmit channels. The problem is solved iteratively with following procedure: Step 1: The $$$B$$$ matrix is updated using a conventional parallel pulse design algorithm. Step 2: Soft thresholding is applied to the $$$B$$$ matrix to minimize its $$$L1$$$ norm. [3]. Step 3: Coil-channel assignments are made by calculating and sorting the $$$L2$$$ norm of each column of $$$B$$$, and assigning every other coil in the sorted list to the next channel. This assignment strategy ensures that the compressed array’s degrees of freedom are spent on the most important coil elements. Step 4: SVD truncation is applied to reduce the rank of each matrix $$$B(\Theta_i)$$$ to 1. This process is repeated until the cost function stops decreasing, yielding the pulse waveforms, the array compression weights, and the coil-channel assignments. Unnecessary coils can be optionally pruned according to the amplitudes of their array compression weights.

METHODS

To validate whether the proposed algorithm yields the best possible coil combinations, pulse designs were performed using simulated $$$B_1^+$$$ maps from a 7T 8 coil head transmit array [4]. AcpTx Pulses with $$$N_{chan} = 2$$$ were designed for the array using the proposed algorithm and compared to pulses designed using all other possible 8 coil-to-2 channel assignments. Three pTx pulse types were designed: (1) Reduced FOV spiral excitations with R = 3.6 acceleration [5], (2) Slice-specific multiband RF shims [6], and (3) Small-tip-angle $$$k_T$$$ points excitations [7]. The algorithm was then used to optimally compress large transmit coil arrays for two applications, and the performance of the compressed arrays was compared to application-specific arrays for which $$$N_{chan} = N_{coils}$$$. The first application was slice-specific multiband RF shimming, with an initial 24-loop array (Fig. 2b) compressed to 8 channels. The acpTx shims were compared to shims designed for the multiband-specific 8-coil array in [8] (Fig. 2a). The second application was selective excitation of the human occipital lobe with a 3D SPINS pulse [9], with an initial 36-loop array (Fig. 2d, with and without pruning down to 8 coils) compressed to 2 channels. The acpTx pulses were compared to pulses designed for a standard 2-coil array (Fig. 2c).

RESULTS

Figure 3 shows that the proposed algorithm identifies the coil assignments with the lowest or near-lowest cost in all the pulse design scenarios, and that these combinations have significantly lower cost than previously-proposed sequential or interleaved coil assignments [1]. In both the multiband and occipital lobe imaging applications, the compressed coil arrays and pulses achieved lower NRMSE, lower total deposited RF power, and lower maximum 10g SAR (Figs. 4 and 5a,b) than the conventional coils. In the occipital excitation case, the algorithm pruned the original 36-coil array down to 8-coils while still maintaining better performance than the 2-coil array. Figure 5c shows that the coils remaining after pruning were at the back of the head, as would be expected.

DISCUSSION & CONCLUSION

This study demonstrated an acpTx pulse design algorithm with optimal coil-to-channel assignments, which enables acpTx with reduced hardware sophistication. It was further shown in the occipital lobe excitation that the algorithm can identify the most important coil elements from a large set of candidate coils, and that the resulting arrays can outperform conventional arrays with the same number of input channels. This may have significant implications for pTx array design and optimization.

Acknowledgements

This work was supported by NIH R01 EB 016695.

References

1. Cao, Z., Yan, X. and Grissom, W. A. (2015), Array-compressed parallel transmit pulse design. Magn Reson Med. doi: 10.1002/mrm.26020.

2. Floser M, Bitz AK, Jost S, Orzada S, Gratz M, Kraff O, Ladd ME. Hybrids of static and dynamic RF shimming for body imaging at 7T. In Proceedings of the 23rd Scienti?c Meeting, International Society for Magnetic Resonance in Medicine, Toronto, Canada, 2015. p. 2391.

3. Zelinski AC, Alagappan VA, Goyal VK, Adalsteinsson E, Wald LL. Sparsity-Enforced Coil Array Mode Compression for Parallel Transmission. In Proceedings of the 16th Scienti?c Meeting, International Society for Magnetic Resonance in Medicine, Toronto, Canada, 2008. p. 1302.

4. Cao, Z., Park, J., Cho, Z.-H. and Collins, C. M. (2015), Numerical evaluation of image homogeneity, signal-to-noise ratio, and specific absorption rate for human brain imaging at 1.5, 3, 7, 10.5, and 14T in an 8-channel transmit/receive array. J. Magn. Reson. Imaging, 41: 1432–1439. doi: 10.1002/jmri.24689.

5. Grissom, W., Yip, C.-y., Zhang, Z., Stenger, V. A., Fessler, J. A. and Noll, D. C. (2006), Spatial domain method for the design of RF pulses in multicoil parallel excitation. Magn Reson Med, 56: 620–629. doi: 10.1002/mrm.20978.

6. X. Wu, S. Schmitter, E. J. Auerbach, S. Moeller, K. U ?gurbil, and P. F. Van de Moortele. Simultane- ous multislice multiband parallel radiofrequency excitation with independent slice-specific transmit B1 homogenization. Magn Reson Med, 70(3):630–638, 2013.

7. Cloos MA, Boulant N, Luong M, Ferrand G, Giacomini E, Le Bihan D, Amadon A. kT-Points: Short three-dimensional tailored RF pulses for ?ip-angle homogenization over an extended volume. Magn Reson Med 2011;67:72–80.

8. Poser, B. A., Anderson, R. J., Guérin, B., Setsompop, K., Deng, W., Mareyam, A., Serano, P., Wald, L. L. and Stenger, V. A. (2014), Simultaneous multislice excitation by parallel transmission. Magn Reson Med, 71: 1416–1427. doi: 10.1002/mrm.24791

9. Malik, S. J., Keihaninejad, S., Hammers, A. and Hajnal, J. V. (2012), Tailored excitation in 3D with spiral nonselective (SPINS) RF pulses. Magn Reson Med, 67: 1303–1315. doi: 10.1002/mrm.23118.

Figures

Figure 1: The array-compressed parallel transmission (acpTx) system configuration that was proposed in Ref. [2] and used in this work.

Fig 2. Coil simulation setup for multiband RF shim designs (A,B) and occipital lobe-selective SPINS pulse designs (C,D).

Fig 3. Histograms of the pulse design cost function Φ(B) for each of the three pTx pulse types, when designing 8 coil-to-2 channel acpTx pulses.

Fig 4. Total B1+ patterns after slice-specific RF shimming for multiband excitation in 3 representative slices, and the corresponding errors, powers and SAR. The top row shows results for all 8 coils of the conventional array, and the bottom row shows results for the acpTx 24-to-8 channel array.

Fig 5. Occipital lobe-selective SPINS pulse design results. (A) Excitation patterns moving up through the brain produced by conventional 2-coil pTx pulses (top row) and 36-coil-to-2-channel acpTx pulses (bottom row). (B) Metrics for the three pulse designs (conventional 2-coil, acpTx 36 coils-to-2 channels, and 36 coils pruned to 8-coils-to-2 channels). (C) Central slice |B1+| Maps of the coils remaining after pruning 36-to-8 coils.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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